- September 11, Seminar for Women in Mathematics at UIUC (50 mins).
Title: Asymptotic translation lengths in the complex of curves.
Abstract: In 1981, Harvey introduced the complex of curves C(S) which captures the combinatorial structure of a surface S. There is a natural action of the mapping class group Mod(S) on C(S), hence we can define asymptotic translation lengths of Mod(S) in C(S) equipped with a metric. We will show that the infinimum length goes to zero like 1/g^2. This talk will be accessible to a general audience. (This is joint work with Vaibhav Gadre).
- June 19, School before Dynamics and Geometry of Teichmuller Space (honoring the 60th birthday of Howard Masur) (20 mins) at Luminy, France. PDF
Title: Introduction of pseudo-Anosov mapping classes.
- April 17-19, RTG Workshop on Geometric Group Theory at Ann Arbor, MI (30 mins)-invited talk. PDF
Title: Asymptotics of least pseudo-Anosov dilatations.
Abstract: The mapping class group of S is the set of all surface homeomorphisms of S up to isotopy. The Nielsen-Thurston classification says that a mapping class is either periodic, reducible, or pseudo-Anosov. Each pseudo-Anosov mapping class is equipped with a real number >1 called the dilatation. We will consider the least dilatation for each surface. In this talk, we will discuss the asymptotic behavior of least pseudo-Anosov dilatations when we vary genus and the number of marked points of a surface.
- April 7, Dynamics Seminar at University of Chicago (60 mins)-invited talk.
Title:Asymptotics of least pseudo-Anosov dilatations.
Abstract: Take the set of all surface homeomorphisms of S up to isotopy. This turns out to be a group which we call the mapping class group, denoted by Mod(S). The Nielsen-Thurston classification says that a mapping class is either periodic, reducible, or pseudo-Anosov. Pseudo-Anosov mapping classes have been the subject of much study. Each pseudo-Anosov mapping class is equipped with a real number >1 called the dilatation. These dilatations provide information on the dynamics of surface homeomorphisms. We will consider the least dilatation for each surface. In this talk, we will see how the behavior of these pseudo-Anosov dilatations depend on the topology of the underlying surface.
- April 2-4, IMA Special Workshop-"Career Options for Women in Mathematical Sciences
" at Minneapolis, MN.
Poster session (Poster, 2-min AD)
Title: The most interesting surface maps.
Abstract: One way to study non-Euclidean geometry is to understand maps of a surface onto itself. Among these maps, the most interesting ones are pseudo-Anosov maps. People has been trying to understand what pseudo-Anosov maps do to a surface. On the other hand, we can try to study how pseudo-Anosov maps behave when we change the underlying surface.
- March 27-29, AMS Sectional meeting "Hyperbolic geometry and Teichmuller theory" (20 mins). PDF
Title: Asymptotics of pseudo-Anosov dilatations.
Abstract: In the talk, we will discuss the asymptotic behavior of least pseudo-Anosov dilatations when we vary genus and the number of marked points of a surface.
- March 20, Seminar for Women in Mathematics at UIUC (50 mins).
Title: From your closet to Teichmuller space.
Abstract: This will be an introduction to Teichmuller space and the mapping class group. Instead of giving definitions, I will explain how to "see" the space. Continuing the same idea, we will see how the mapping class group acts on Teichmuller space. In particular, we will talk about the action of pseudo-Anosov mapping classes, which are non-periodic and irreducible. To obtain more intuition, I will construct some pseudo-Anosov mapping classes. On the other hand, we will use couple methods to check if a given mapping class is pseudo-Anosov.
- November 20, Group Theory Semina at UIUC (50 mins).
Title: A homomorphism between a subgroup of Mod(S) and PSL(2,R)
Abstract: Let G be a subgroup of Mod(S) generated by Dehn multitwists T_a and T_b, where a and b are unions of disjoint essential simple closed curves, and the union of a and b fills S. In the talk, we will discuss Thurston's construction of a homomorphism from G to PSL(2,R). In particular, there is a correspondence between the type of a mapping class in G and the type of its image. If time is allowed, we will see a few examples using this property.
- June 14-20, MRC:Teichmiller Theory & Low dimensional topology (5-7 mins). PDF
- May 12-23, Institute for Advanced Study (IAS) "Women and Mathematics program" (40 mins). PDF
- April 1, Seminar for Women in Mathematics at UIUC (50 mins).
Title: Bounds for a least pseudo-Anosov dilatation
Abstract: A current area of interest in hyperbolic two-manifolds is understanding pseudo-Anosov homeomorphisms. First I will explain what pseudo-Anosov dilatations mean. Since dilatations of a surface S form a discrete set, it has a minimal element, which we call the least pseudo-Anosov dilatation of S. I will give you known results of bounds for some surfaces S. After that, I will state my main theorem, bounds for a least pseudo-Anosov dilatation of a genus(>1) surface with punctures, then I will give a proof of the upper bound.